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The Maximin Principle

Of all the principles the simplest the simplest is the maximin principle for determining an optimal action when consequences are given in terms of profits. According to this principle the decision-maker first observes the minimum payoff is maximum. This principle places a value on each action according to the worst that can happen with the action. In a sense, decision-maker expects worst and prepares for it. Symbolically, the maximization is that which maximizes the min pik. Let us apply this principle to Illustration 1 and 2 for finding optimal action. The
Min pi1 = minimum payoff for fixed action a1 = 156
Min pi2 = minimum payoff for fixed action a2 = 153
Min pi3 = minimum payoff for fixed action a3 = 150
These minimum payoffs are maximum for action a1. Hence the principle suggests the decision-maker to take action a1. The maximum action is a1 = production of 78 pastries.

The minimum payoffs over the various states of nature are given below:
Min pi1 = - 100
Min pi2 = - 500 ________[:. Minimum values occur when θ1 = 100]

Clearly, the minimum payoff is maximum for action a1 (since – 100> - 500). Hence the maximum action in a1 = junk the lot at a loss or Rs. 100.

The maximum principle discussed above usually requires a considerable about of computation. Furthermore, a serious objection is that it is generally too pessimistic since the decision-maker chooses that state of nature for which his payoffs are minimum.

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